diff --git a/Advanced/Introduction to Quantum/src/parts/01 bits.tex b/Advanced/Introduction to Quantum/src/parts/01 bits.tex index 4c21c54..ba444dc 100644 --- a/Advanced/Introduction to Quantum/src/parts/01 bits.tex +++ b/Advanced/Introduction to Quantum/src/parts/01 bits.tex @@ -462,48 +462,24 @@ Thus, \end{equation*} -\begin{ORMCbox}{Review: Matrix Multiplication}{black!10!white}{black!65!white} - Matrix multiplication works as follows: - +\begin{ORMCbox}{Review: Multiplying Vectors by Matrices}{black!10!white}{black!65!white} \begin{equation*} - AB = + Av = \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ \end{bmatrix} \begin{bmatrix} - a_0 & b_0 \\ - a_1 & b_1 \\ + v_0 \\ v_1 \end{bmatrix} = \begin{bmatrix} - 1a_0 + 2a_1 & 1b_0 + 2b_1 \\ - 3a_0 + 4a_1 & 3b_0 + 4b_1 \\ + 1v_0 + 2v_1 \\ + 3v_0 + 4v_1 \end{bmatrix} \end{equation*} - - Note that this is very similar to multiplying each column of $B$ by $A$. \par - The product $AB$ is simply $Ac$ for every column $c$ in $B$: - - \begin{equation*} - Ac_0 = - \begin{bmatrix} - 1 & 2 \\ - 3 & 4 \\ - \end{bmatrix} - \begin{bmatrix} - a_0 \\ a_1 - \end{bmatrix} - = - \begin{bmatrix} - 1a_0 + 2a_1 \\ - 3a_0 + 4a_1 - \end{bmatrix} - \end{equation*} - - This is exactly the first column of the matrix product. \par - Also, note that each element of $Ac_0$ is the dot product of a row in $A$ and a column in $c_0$. + Note that each element of $Av$ is the dot product of a row in $A$ and a column in $v$. \end{ORMCbox} \problem{}